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<a href="classEigen_1_1CompleteOrthogonalDecomposition-members.html">List of all members</a> &#124;
<a href="#pub-methods">Public Member Functions</a> &#124;
<a href="#pro-methods">Protected Member Functions</a>  </div>
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<div class="title">Eigen::CompleteOrthogonalDecomposition&lt; MatrixType_ &gt; Class Template Reference<div class="ingroups"><a class="el" href="group__DenseLinearSolvers__chapter.html">Dense linear problems and decompositions</a> &raquo; <a class="el" href="group__DenseLinearSolvers__Reference.html">Reference</a> &raquo; <a class="el" href="group__QR__Module.html">QR module</a></div></div>  </div>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><h3>template&lt;typename MatrixType_&gt;<br />
class Eigen::CompleteOrthogonalDecomposition&lt; MatrixType_ &gt;</h3>

<p>Complete orthogonal decomposition (COD) of a matrix. </p>
<dl class="tparams"><dt>Template Parameters</dt><dd>
  <table class="tparams">
    <tr><td class="paramname">MatrixType_</td><td>the type of the matrix of which we are computing the COD.</td></tr>
  </table>
  </dd>
</dl>
<p>This class performs a rank-revealing complete orthogonal decomposition of a matrix <b>A</b> into matrices <b>P</b>, <b>Q</b>, <b>T</b>, and <b>Z</b> such that </p><p class="formulaDsp">
\[ \mathbf{A} \, \mathbf{P} = \mathbf{Q} \, \begin{bmatrix} \mathbf{T} &amp; \mathbf{0} \\ \mathbf{0} &amp; \mathbf{0} \end{bmatrix} \, \mathbf{Z} \]
</p>
<p> by using Householder transformations. Here, <b>P</b> is a permutation matrix, <b>Q</b> and <b>Z</b> are unitary matrices and <b>T</b> an upper triangular matrix of size rank-by-rank. <b>A</b> may be rank deficient.</p>
<p>This class supports the <a class="el" href="group__InplaceDecomposition.html">inplace decomposition </a> mechanism.</p>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1MatrixBase.html#ae90b6846f05bd30b8d52b66e427e3e09">MatrixBase::completeOrthogonalDecomposition()</a> </dd></dl>
</div><div id="dynsection-0" onclick="return toggleVisibility(this)" class="dynheader closed" style="cursor:pointer;">
  <img id="dynsection-0-trigger" src="closed.png" alt="+"/> Inheritance diagram for Eigen::CompleteOrthogonalDecomposition&lt; MatrixType_ &gt;:</div>
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<div class="center"><img src="classEigen_1_1CompleteOrthogonalDecomposition__inherit__graph.png" border="0" usemap="#aEigen_1_1CompleteOrthogonalDecomposition_3_01MatrixType___01_4_inherit__map" alt="Inheritance graph"/></div>
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<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:ac040c34ce3fb2b68d3f57adc0c29d526"><td class="memItemLeft" align="right" valign="top">MatrixType::RealScalar&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#ac040c34ce3fb2b68d3f57adc0c29d526">absDeterminant</a> () const</td></tr>
<tr class="separator:ac040c34ce3fb2b68d3f57adc0c29d526"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a284b4bb5ad267837056119f533bc7752"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1PermutationMatrix.html">PermutationType</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a284b4bb5ad267837056119f533bc7752">colsPermutation</a> () const</td></tr>
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<tr class="memitem:a8a94c3d01d207ef16aa2177a2b0c5953"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a8a94c3d01d207ef16aa2177a2b0c5953">CompleteOrthogonalDecomposition</a> ()</td></tr>
<tr class="memdesc:a8a94c3d01d207ef16aa2177a2b0c5953"><td class="mdescLeft">&#160;</td><td class="mdescRight">Default Constructor.  <a href="classEigen_1_1CompleteOrthogonalDecomposition.html#a8a94c3d01d207ef16aa2177a2b0c5953">More...</a><br /></td></tr>
<tr class="separator:a8a94c3d01d207ef16aa2177a2b0c5953"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a94e1eb8a57d1e604b61a73a510ded439"><td class="memTemplParams" colspan="2">template&lt;typename InputType &gt; </td></tr>
<tr class="memitem:a94e1eb8a57d1e604b61a73a510ded439"><td class="memTemplItemLeft" align="right" valign="top">&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a94e1eb8a57d1e604b61a73a510ded439">CompleteOrthogonalDecomposition</a> (const <a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; InputType &gt; &amp;matrix)</td></tr>
<tr class="memdesc:a94e1eb8a57d1e604b61a73a510ded439"><td class="mdescLeft">&#160;</td><td class="mdescRight">Constructs a complete orthogonal decomposition from a given matrix.  <a href="classEigen_1_1CompleteOrthogonalDecomposition.html#a94e1eb8a57d1e604b61a73a510ded439">More...</a><br /></td></tr>
<tr class="separator:a94e1eb8a57d1e604b61a73a510ded439"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae7ff6ebc9b83cbe7617b29940c4a3744"><td class="memTemplParams" colspan="2">template&lt;typename InputType &gt; </td></tr>
<tr class="memitem:ae7ff6ebc9b83cbe7617b29940c4a3744"><td class="memTemplItemLeft" align="right" valign="top">&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#ae7ff6ebc9b83cbe7617b29940c4a3744">CompleteOrthogonalDecomposition</a> (<a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; InputType &gt; &amp;matrix)</td></tr>
<tr class="memdesc:ae7ff6ebc9b83cbe7617b29940c4a3744"><td class="mdescLeft">&#160;</td><td class="mdescRight">Constructs a complete orthogonal decomposition from a given matrix.  <a href="classEigen_1_1CompleteOrthogonalDecomposition.html#ae7ff6ebc9b83cbe7617b29940c4a3744">More...</a><br /></td></tr>
<tr class="separator:ae7ff6ebc9b83cbe7617b29940c4a3744"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ad8910c5d4d52bc29ecda801bd9acf10e"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#ad8910c5d4d52bc29ecda801bd9acf10e">CompleteOrthogonalDecomposition</a> (<a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> rows, <a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> cols)</td></tr>
<tr class="memdesc:ad8910c5d4d52bc29ecda801bd9acf10e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Default Constructor with memory preallocation.  <a href="classEigen_1_1CompleteOrthogonalDecomposition.html#ad8910c5d4d52bc29ecda801bd9acf10e">More...</a><br /></td></tr>
<tr class="separator:ad8910c5d4d52bc29ecda801bd9acf10e"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aa86b911cf8754fb172804966b04e6013"><td class="memItemLeft" align="right" valign="top"><a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#aa86b911cf8754fb172804966b04e6013">dimensionOfKernel</a> () const</td></tr>
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<tr class="memitem:af0ede3cbb5e2878daa1a148bd3943917"><td class="memItemLeft" align="right" valign="top">const HCoeffsType &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#af0ede3cbb5e2878daa1a148bd3943917">hCoeffs</a> () const</td></tr>
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<tr class="memitem:ac95b93ddad59c6e57d06fcd4737b27e1"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1HouseholderSequence.html">HouseholderSequenceType</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#ac95b93ddad59c6e57d06fcd4737b27e1">householderQ</a> (void) const</td></tr>
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<tr class="memitem:a3521b66f1b597a2e18b13ab542cd48f4"><td class="memItemLeft" align="right" valign="top"><a class="el" href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a3521b66f1b597a2e18b13ab542cd48f4">info</a> () const</td></tr>
<tr class="memdesc:a3521b66f1b597a2e18b13ab542cd48f4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Reports whether the complete orthogonal decomposition was successful.  <a href="classEigen_1_1CompleteOrthogonalDecomposition.html#a3521b66f1b597a2e18b13ab542cd48f4">More...</a><br /></td></tr>
<tr class="separator:a3521b66f1b597a2e18b13ab542cd48f4"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a381e9c1cbb5660821554fedb3d347f5d"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a381e9c1cbb5660821554fedb3d347f5d">isInjective</a> () const</td></tr>
<tr class="separator:a381e9c1cbb5660821554fedb3d347f5d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a2e1e4c484ee28a89fa821313d18691fb"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a2e1e4c484ee28a89fa821313d18691fb">isInvertible</a> () const</td></tr>
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<tr class="memitem:a52030f2aeb90d4eba8203635bf7fbec4"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a52030f2aeb90d4eba8203635bf7fbec4">isSurjective</a> () const</td></tr>
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<tr class="memitem:ad59d6dc78dab52a0038ac372b4a72c0d"><td class="memItemLeft" align="right" valign="top">MatrixType::RealScalar&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#ad59d6dc78dab52a0038ac372b4a72c0d">logAbsDeterminant</a> () const</td></tr>
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<tr class="memitem:ae25bc71f3cbc01da5f63c30eed12e5c4"><td class="memItemLeft" align="right" valign="top">const MatrixType &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#ae25bc71f3cbc01da5f63c30eed12e5c4">matrixQTZ</a> () const</td></tr>
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<tr class="memitem:a8f0580429cdba56ea1fd7ae5f8d48774"><td class="memItemLeft" align="right" valign="top">const MatrixType &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a8f0580429cdba56ea1fd7ae5f8d48774">matrixT</a> () const</td></tr>
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<tr class="memitem:a4206a90976d04c4275301b308108f60b"><td class="memItemLeft" align="right" valign="top">MatrixType&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a4206a90976d04c4275301b308108f60b">matrixZ</a> () const</td></tr>
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<tr class="memitem:ac0e5f2123e375c181e28db748ce2b1c8"><td class="memItemLeft" align="right" valign="top">RealScalar&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#ac0e5f2123e375c181e28db748ce2b1c8">maxPivot</a> () const</td></tr>
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<tr class="memitem:a1897953269e238eacea58afc3307958b"><td class="memItemLeft" align="right" valign="top"><a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a1897953269e238eacea58afc3307958b">nonzeroPivots</a> () const</td></tr>
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<tr class="memitem:ab5e8b3f2c7b602772e1f1d7ce63d446e"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Inverse.html">Inverse</a>&lt; <a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html">CompleteOrthogonalDecomposition</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#ab5e8b3f2c7b602772e1f1d7ce63d446e">pseudoInverse</a> () const</td></tr>
<tr class="separator:ab5e8b3f2c7b602772e1f1d7ce63d446e"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a0ea6a40374c16331f8d323d1f64bf57e"><td class="memItemLeft" align="right" valign="top"><a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a0ea6a40374c16331f8d323d1f64bf57e">rank</a> () const</td></tr>
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<tr class="memitem:a8fa642ffb4181e550a593d71fc0d03bf"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html">CompleteOrthogonalDecomposition</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a8fa642ffb4181e550a593d71fc0d03bf">setThreshold</a> (const RealScalar &amp;<a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a16c1fd97a7ef99d1cf64f8cf1ee81cbf">threshold</a>)</td></tr>
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<tr class="memitem:a416920738f4f132694b9f42029290402"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html">CompleteOrthogonalDecomposition</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a416920738f4f132694b9f42029290402">setThreshold</a> (Default_t)</td></tr>
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<tr class="memitem:a6958a5faddd8f8479eb364017968833c"><td class="memTemplParams" colspan="2">template&lt;typename Rhs &gt; </td></tr>
<tr class="memitem:a6958a5faddd8f8479eb364017968833c"><td class="memTemplItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Solve.html">Solve</a>&lt; <a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html">CompleteOrthogonalDecomposition</a>, Rhs &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a6958a5faddd8f8479eb364017968833c">solve</a> (const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>&lt; Rhs &gt; &amp;b) const</td></tr>
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<tr class="memitem:a16c1fd97a7ef99d1cf64f8cf1ee81cbf"><td class="memItemLeft" align="right" valign="top">RealScalar&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a16c1fd97a7ef99d1cf64f8cf1ee81cbf">threshold</a> () const</td></tr>
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<tr class="memitem:a16e3f4b982e1e3506e419761a3ec96f8"><td class="memItemLeft" align="right" valign="top">const HCoeffsType &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a16e3f4b982e1e3506e419761a3ec96f8">zCoeffs</a> () const</td></tr>
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<tr class="inherit_header pub_methods_classEigen_1_1SolverBase"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_classEigen_1_1SolverBase')"><img src="closed.png" alt="-"/>&#160;Public Member Functions inherited from <a class="el" href="classEigen_1_1SolverBase.html">Eigen::SolverBase&lt; CompleteOrthogonalDecomposition&lt; MatrixType_ &gt; &gt;</a></td></tr>
<tr class="memitem:ae1025416bdb5a768f7213c67feb4dc33 inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">const AdjointReturnType&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#ae1025416bdb5a768f7213c67feb4dc33">adjoint</a> () const</td></tr>
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<tr class="memitem:a1fbabe7f12bcbfba3b9a448b1f5e46fa inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html">CompleteOrthogonalDecomposition</a>&lt; MatrixType_ &gt; &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a> ()</td></tr>
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<tr class="memitem:afd4f3f1c57b7594b96a7e30f2974ea2e inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html">CompleteOrthogonalDecomposition</a>&lt; MatrixType_ &gt; &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#afd4f3f1c57b7594b96a7e30f2974ea2e">derived</a> () const</td></tr>
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<tr class="memitem:a7fd647d110487799205df6f99547879d inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Solve.html">Solve</a>&lt; <a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html">CompleteOrthogonalDecomposition</a>&lt; MatrixType_ &gt;, Rhs &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#a7fd647d110487799205df6f99547879d">solve</a> (const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>&lt; Rhs &gt; &amp;b) const</td></tr>
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<tr class="memitem:a4d5e5baddfba3790ab1a5f247dcc4dc1 inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#a4d5e5baddfba3790ab1a5f247dcc4dc1">SolverBase</a> ()</td></tr>
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<tr class="memitem:a70cf5cd1b31dbb4f4d61c436c83df6d3 inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Transpose.html">ConstTransposeReturnType</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#a70cf5cd1b31dbb4f4d61c436c83df6d3">transpose</a> () const</td></tr>
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<tr class="inherit_header pub_methods_structEigen_1_1EigenBase"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_structEigen_1_1EigenBase')"><img src="closed.png" alt="-"/>&#160;Public Member Functions inherited from <a class="el" href="structEigen_1_1EigenBase.html">Eigen::EigenBase&lt; Derived &gt;</a></td></tr>
<tr class="memitem:a2d768a9877f5f69f49432d447b552bfe inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">EIGEN_CONSTEXPR <a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#a2d768a9877f5f69f49432d447b552bfe">cols</a> () const EIGEN_NOEXCEPT</td></tr>
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<tr class="memitem:a1fbabe7f12bcbfba3b9a448b1f5e46fa inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">Derived &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a> ()</td></tr>
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<tr class="memitem:afd4f3f1c57b7594b96a7e30f2974ea2e inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">const Derived &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#afd4f3f1c57b7594b96a7e30f2974ea2e">derived</a> () const</td></tr>
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<tr class="memitem:ac22eb0695d00edd7d4a3b2d0a98b81c2 inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">EIGEN_CONSTEXPR <a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a> () const EIGEN_NOEXCEPT</td></tr>
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<tr class="memitem:ae106171b6fefd3f7af108a8283de36c9 inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">EIGEN_CONSTEXPR <a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#ae106171b6fefd3f7af108a8283de36c9">size</a> () const EIGEN_NOEXCEPT</td></tr>
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Protected Member Functions</h2></td></tr>
<tr class="memitem:a0a89641e0b4ea92c515405f2a31e6abe"><td class="memTemplParams" colspan="2">template&lt;typename Rhs &gt; </td></tr>
<tr class="memitem:a0a89641e0b4ea92c515405f2a31e6abe"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a0a89641e0b4ea92c515405f2a31e6abe">applyZAdjointOnTheLeftInPlace</a> (Rhs &amp;rhs) const</td></tr>
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<tr class="memitem:afedd1ee41b8490b70fd1fefdd21f8c80"><td class="memTemplParams" colspan="2">template&lt;bool Conjugate, typename Rhs &gt; </td></tr>
<tr class="memitem:afedd1ee41b8490b70fd1fefdd21f8c80"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#afedd1ee41b8490b70fd1fefdd21f8c80">applyZOnTheLeftInPlace</a> (Rhs &amp;rhs) const</td></tr>
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<tr class="memitem:adb0b963d7d8f96492904e8eda03efbf5"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#adb0b963d7d8f96492904e8eda03efbf5">computeInPlace</a> ()</td></tr>
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Additional Inherited Members</h2></td></tr>
<tr class="inherit_header pub_types_structEigen_1_1EigenBase"><td colspan="2" onclick="javascript:toggleInherit('pub_types_structEigen_1_1EigenBase')"><img src="closed.png" alt="-"/>&#160;Public Types inherited from <a class="el" href="structEigen_1_1EigenBase.html">Eigen::EigenBase&lt; Derived &gt;</a></td></tr>
<tr class="memitem:a554f30542cc2316add4b1ea0a492ff02 inherit pub_types_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a></td></tr>
<tr class="memdesc:a554f30542cc2316add4b1ea0a492ff02 inherit pub_types_structEigen_1_1EigenBase"><td class="mdescLeft">&#160;</td><td class="mdescRight">The interface type of indices.  <a href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">More...</a><br /></td></tr>
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<h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a8a94c3d01d207ef16aa2177a2b0c5953">&#9670;&nbsp;</a></span>CompleteOrthogonalDecomposition() <span class="overload">[1/4]</span></h2>

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<p>Default Constructor. </p>
<p>The default constructor is useful in cases in which the user intends to perform decompositions via <code>CompleteOrthogonalDecomposition::compute(const* MatrixType&amp;)</code>. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#ad8910c5d4d52bc29ecda801bd9acf10e">&#9670;&nbsp;</a></span>CompleteOrthogonalDecomposition() <span class="overload">[2/4]</span></h2>

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          <td>(</td>
          <td class="paramtype"><a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td>
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<p>Default Constructor with memory preallocation. </p>
<p>Like the default constructor but with preallocation of the internal data according to the specified problem <em>size</em>. </p><dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a8a94c3d01d207ef16aa2177a2b0c5953" title="Default Constructor.">CompleteOrthogonalDecomposition()</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a94e1eb8a57d1e604b61a73a510ded439">&#9670;&nbsp;</a></span>CompleteOrthogonalDecomposition() <span class="overload">[3/4]</span></h2>

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<p>Constructs a complete orthogonal decomposition from a given matrix. </p>
<p>This constructor computes the complete orthogonal decomposition of the matrix <em>matrix</em> by calling the method compute(). The default threshold for rank determination will be used. It is a short cut for:</p>
<div class="fragment"><div class="line">CompleteOrthogonalDecomposition&lt;MatrixType&gt; cod(matrix.rows(),</div>
<div class="line">                                                matrix.cols());</div>
<div class="line">cod.setThreshold(Default);</div>
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</div><!-- fragment --><dl class="section see"><dt>See also</dt><dd>compute() </dd></dl>

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<p>Constructs a complete orthogonal decomposition from a given matrix. </p>
<p>This overloaded constructor is provided for <a class="el" href="group__InplaceDecomposition.html">inplace decomposition </a> when <code>MatrixType</code> is a <a class="el" href="classEigen_1_1Ref.html" title="A matrix or vector expression mapping an existing expression.">Eigen::Ref</a>.</p>
<dl class="section see"><dt>See also</dt><dd>CompleteOrthogonalDecomposition(const EigenBase&amp;) </dd></dl>

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<h2 class="groupheader">Member Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#ac040c34ce3fb2b68d3f57adc0c29d526">&#9670;&nbsp;</a></span>absDeterminant()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the absolute value of the determinant of the matrix of which *this is the complete orthogonal decomposition. It has only linear complexity (that is, O(n) where n is the dimension of the square matrix) as the complete orthogonal decomposition has already been computed.</dd></dl>
<dl class="section note"><dt>Note</dt><dd>This is only for square matrices.</dd></dl>
<dl class="section warning"><dt>Warning</dt><dd>a determinant can be very big or small, so for matrices of large enough dimension, there is a risk of overflow/underflow. One way to work around that is to use <a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#ad59d6dc78dab52a0038ac372b4a72c0d">logAbsDeterminant()</a> instead.</dd></dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#ad59d6dc78dab52a0038ac372b4a72c0d">logAbsDeterminant()</a>, <a class="el" href="classEigen_1_1MatrixBase.html#a7ad8f77004bb956b603bb43fd2e3c061">MatrixBase::determinant()</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a0a89641e0b4ea92c515405f2a31e6abe">&#9670;&nbsp;</a></span>applyZAdjointOnTheLeftInPlace()</h2>

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<p>Overwrites <b>rhs</b> with \( \mathbf{Z}^* * \mathbf{rhs} \). </p>

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<h2 class="memtitle"><span class="permalink"><a href="#afedd1ee41b8490b70fd1fefdd21f8c80">&#9670;&nbsp;</a></span>applyZOnTheLeftInPlace()</h2>

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<p>Overwrites <b>rhs</b> with \( \mathbf{Z} * \mathbf{rhs} \) or \( \mathbf{\overline Z} * \mathbf{rhs} \) if <code>Conjugate</code> is set to <code>true</code>. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a284b4bb5ad267837056119f533bc7752">&#9670;&nbsp;</a></span>colsPermutation()</h2>

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<dl class="section return"><dt>Returns</dt><dd>a const reference to the column permutation matrix </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#adb0b963d7d8f96492904e8eda03efbf5">&#9670;&nbsp;</a></span>computeInPlace()</h2>

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<p>Performs the complete orthogonal decomposition of the given matrix <em>matrix</em>. The result of the factorization is stored into <code>*this</code>, and a reference to <code>*this</code> is returned.</p>
<dl class="section see"><dt>See also</dt><dd>class <a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html" title="Complete orthogonal decomposition (COD) of a matrix.">CompleteOrthogonalDecomposition</a>, CompleteOrthogonalDecomposition(const MatrixType&amp;) </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#aa86b911cf8754fb172804966b04e6013">&#9670;&nbsp;</a></span>dimensionOfKernel()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the dimension of the kernel of the matrix of which *this is the complete orthogonal decomposition.</dd></dl>
<dl class="section note"><dt>Note</dt><dd>This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling <a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a8fa642ffb4181e550a593d71fc0d03bf">setThreshold(const RealScalar&amp;)</a>. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#af0ede3cbb5e2878daa1a148bd3943917">&#9670;&nbsp;</a></span>hCoeffs()</h2>

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<dl class="section return"><dt>Returns</dt><dd>a const reference to the vector of Householder coefficients used to represent the factor <code>Q</code>.</dd></dl>
<p>For advanced uses only. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#ac95b93ddad59c6e57d06fcd4737b27e1">&#9670;&nbsp;</a></span>householderQ()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the matrix Q as a sequence of householder transformations </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a3521b66f1b597a2e18b13ab542cd48f4">&#9670;&nbsp;</a></span>info()</h2>

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<p>Reports whether the complete orthogonal decomposition was successful. </p>
<dl class="section note"><dt>Note</dt><dd>This function always returns <code>Success</code>. It is provided for compatibility with other factorization routines. </dd></dl>
<dl class="section return"><dt>Returns</dt><dd><code>Success</code> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a381e9c1cbb5660821554fedb3d347f5d">&#9670;&nbsp;</a></span>isInjective()</h2>

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<dl class="section return"><dt>Returns</dt><dd>true if the matrix of which *this is the decomposition represents an injective linear map, i.e. has trivial kernel; false otherwise.</dd></dl>
<dl class="section note"><dt>Note</dt><dd>This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling <a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a8fa642ffb4181e550a593d71fc0d03bf">setThreshold(const RealScalar&amp;)</a>. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a2e1e4c484ee28a89fa821313d18691fb">&#9670;&nbsp;</a></span>isInvertible()</h2>

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<dl class="section return"><dt>Returns</dt><dd>true if the matrix of which *this is the complete orthogonal decomposition is invertible.</dd></dl>
<dl class="section note"><dt>Note</dt><dd>This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling <a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a8fa642ffb4181e550a593d71fc0d03bf">setThreshold(const RealScalar&amp;)</a>. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a52030f2aeb90d4eba8203635bf7fbec4">&#9670;&nbsp;</a></span>isSurjective()</h2>

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<dl class="section return"><dt>Returns</dt><dd>true if the matrix of which *this is the decomposition represents a surjective linear map; false otherwise.</dd></dl>
<dl class="section note"><dt>Note</dt><dd>This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling <a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a8fa642ffb4181e550a593d71fc0d03bf">setThreshold(const RealScalar&amp;)</a>. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#ad59d6dc78dab52a0038ac372b4a72c0d">&#9670;&nbsp;</a></span>logAbsDeterminant()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the natural log of the absolute value of the determinant of the matrix of which *this is the complete orthogonal decomposition. It has only linear complexity (that is, O(n) where n is the dimension of the square matrix) as the complete orthogonal decomposition has already been computed.</dd></dl>
<dl class="section note"><dt>Note</dt><dd>This is only for square matrices.</dd>
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This method is useful to work around the risk of overflow/underflow that's inherent to determinant computation.</dd></dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#ac040c34ce3fb2b68d3f57adc0c29d526">absDeterminant()</a>, <a class="el" href="classEigen_1_1MatrixBase.html#a7ad8f77004bb956b603bb43fd2e3c061">MatrixBase::determinant()</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#ae25bc71f3cbc01da5f63c30eed12e5c4">&#9670;&nbsp;</a></span>matrixQTZ()</h2>

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<dl class="section return"><dt>Returns</dt><dd>a reference to the matrix where the complete orthogonal decomposition is stored </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a8f0580429cdba56ea1fd7ae5f8d48774">&#9670;&nbsp;</a></span>matrixT()</h2>

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<dl class="section return"><dt>Returns</dt><dd>a reference to the matrix where the complete orthogonal decomposition is stored. </dd></dl>
<dl class="section warning"><dt>Warning</dt><dd>The strict lower part and<div class="fragment"><div class="line">cols() - <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a0ea6a40374c16331f8d323d1f64bf57e">rank</a>() </div>
<div class="ttc" id="aclassEigen_1_1CompleteOrthogonalDecomposition_html_a0ea6a40374c16331f8d323d1f64bf57e"><div class="ttname"><a href="classEigen_1_1CompleteOrthogonalDecomposition.html#a0ea6a40374c16331f8d323d1f64bf57e">Eigen::CompleteOrthogonalDecomposition::rank</a></div><div class="ttdeci">Index rank() const</div><div class="ttdef"><b>Definition:</b> CompleteOrthogonalDecomposition.h:237</div></div>
</div><!-- fragment --> right columns of this matrix contains internal values. Only the upper triangular part should be referenced. To get it, use <div class="fragment"><div class="line"><a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a8f0580429cdba56ea1fd7ae5f8d48774">matrixT</a>().template triangularView&lt;Upper&gt;() </div>
<div class="ttc" id="aclassEigen_1_1CompleteOrthogonalDecomposition_html_a8f0580429cdba56ea1fd7ae5f8d48774"><div class="ttname"><a href="classEigen_1_1CompleteOrthogonalDecomposition.html#a8f0580429cdba56ea1fd7ae5f8d48774">Eigen::CompleteOrthogonalDecomposition::matrixT</a></div><div class="ttdeci">const MatrixType &amp; matrixT() const</div><div class="ttdef"><b>Definition:</b> CompleteOrthogonalDecomposition.h:185</div></div>
</div><!-- fragment --> For rank-deficient matrices, use <div class="fragment"><div class="line"><a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a8f0580429cdba56ea1fd7ae5f8d48774">matrixT</a>().topLeftCorner(<a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a0ea6a40374c16331f8d323d1f64bf57e">rank</a>(), <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a0ea6a40374c16331f8d323d1f64bf57e">rank</a>()).template triangularView&lt;Upper&gt;()</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a4206a90976d04c4275301b308108f60b">&#9670;&nbsp;</a></span>matrixZ()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the matrix <b>Z</b>. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#ac0e5f2123e375c181e28db748ce2b1c8">&#9670;&nbsp;</a></span>maxPivot()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the absolute value of the biggest pivot, i.e. the biggest diagonal coefficient of R. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a1897953269e238eacea58afc3307958b">&#9670;&nbsp;</a></span>nonzeroPivots()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the number of nonzero pivots in the complete orthogonal decomposition. Here nonzero is meant in the exact sense, not in a fuzzy sense. So that notion isn't really intrinsically interesting, but it is still useful when implementing algorithms.</dd></dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a0ea6a40374c16331f8d323d1f64bf57e">rank()</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#ab5e8b3f2c7b602772e1f1d7ce63d446e">&#9670;&nbsp;</a></span>pseudoInverse()</h2>

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          <td class="memname">const <a class="el" href="classEigen_1_1Inverse.html">Inverse</a>&lt;<a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html">CompleteOrthogonalDecomposition</a>&gt; <a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html">Eigen::CompleteOrthogonalDecomposition</a>&lt; MatrixType_ &gt;::pseudoInverse </td>
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<dl class="section return"><dt>Returns</dt><dd>the pseudo-inverse of the matrix of which *this is the complete orthogonal decomposition. </dd></dl>
<dl class="section warning"><dt>Warning</dt><dd>: Do not compute <code>this-&gt;<a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#ab5e8b3f2c7b602772e1f1d7ce63d446e">pseudoInverse()</a>*rhs</code> to solve a linear systems. It is more efficient and numerically stable to call <code>this-&gt;solve(rhs)</code>. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a0ea6a40374c16331f8d323d1f64bf57e">&#9670;&nbsp;</a></span>rank()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the rank of the matrix of which *this is the complete orthogonal decomposition.</dd></dl>
<dl class="section note"><dt>Note</dt><dd>This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling <a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a8fa642ffb4181e550a593d71fc0d03bf">setThreshold(const RealScalar&amp;)</a>. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a8fa642ffb4181e550a593d71fc0d03bf">&#9670;&nbsp;</a></span>setThreshold() <span class="overload">[1/2]</span></h2>

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<p>Allows to prescribe a threshold to be used by certain methods, such as <a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a0ea6a40374c16331f8d323d1f64bf57e">rank()</a>, who need to determine when pivots are to be considered nonzero. Most be called before calling compute().</p>
<p>When it needs to get the threshold value, <a class="el" href="namespaceEigen.html" title="Namespace containing all symbols from the Eigen library.">Eigen</a> calls <a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a16c1fd97a7ef99d1cf64f8cf1ee81cbf">threshold()</a>. By default, this uses a formula to automatically determine a reasonable threshold. Once you have called the present method <a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a8fa642ffb4181e550a593d71fc0d03bf">setThreshold(const RealScalar&amp;)</a>, your value is used instead.</p>
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<p>A pivot will be considered nonzero if its absolute value is strictly greater than \( \vert pivot \vert \leqslant threshold \times \vert maxpivot \vert \) where maxpivot is the biggest pivot.</p>
<p>If you want to come back to the default behavior, call <a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a416920738f4f132694b9f42029290402">setThreshold(Default_t)</a> </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a416920738f4f132694b9f42029290402">&#9670;&nbsp;</a></span>setThreshold() <span class="overload">[2/2]</span></h2>

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<p>Allows to come back to the default behavior, letting <a class="el" href="namespaceEigen.html" title="Namespace containing all symbols from the Eigen library.">Eigen</a> use its default formula for determining the threshold.</p>
<p>You should pass the special object Eigen::Default as parameter here. </p><div class="fragment"><div class="line">qr.setThreshold(Eigen::Default); </div>
</div><!-- fragment --><p>See the documentation of <a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a8fa642ffb4181e550a593d71fc0d03bf">setThreshold(const RealScalar&amp;)</a>. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a6958a5faddd8f8479eb364017968833c">&#9670;&nbsp;</a></span>solve()</h2>

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<p>This method computes the minimum-norm solution X to a least squares problem </p><p class="formulaDsp">
\[\mathrm{minimize} \|A X - B\|, \]
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<p> where <b>A</b> is the matrix of which <code>*this</code> is the complete orthogonal decomposition.</p>
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<dl class="section return"><dt>Returns</dt><dd>a solution. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a16c1fd97a7ef99d1cf64f8cf1ee81cbf">&#9670;&nbsp;</a></span>threshold()</h2>

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<p>Returns the threshold that will be used by certain methods such as <a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a0ea6a40374c16331f8d323d1f64bf57e">rank()</a>.</p>
<p>See the documentation of <a class="el" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a8fa642ffb4181e550a593d71fc0d03bf">setThreshold(const RealScalar&amp;)</a>. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a16e3f4b982e1e3506e419761a3ec96f8">&#9670;&nbsp;</a></span>zCoeffs()</h2>

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<dl class="section return"><dt>Returns</dt><dd>a const reference to the vector of Householder coefficients used to represent the factor <code>Z</code>.</dd></dl>
<p>For advanced uses only. </p>

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